INMO 1992 Problem 4

Find the number of permutations $( p_1, p_2, p_3 , p_4 , p_5 , p_6)$ of $1, 2 ,3,4,5,6$ such that for any $k, 1 \leq k \leq 5$ , $(p_1, \ldots, p_k)$ does not form a permutation of $1 , 2, \ldots, k$ .